Learning And Teaching

Feynman Learning Technique:
1)  Take a piece of paper and write the concept’s name at the top.
2)  Explain the concept using simple language (show examples to demonstrate you know how the concept works)
3)  Identify problem areas in your explanation or examples and then go back to the sources to review the material / concept
4)  Pinpoint any complicated terms and challenge yourself to simplify them.
Several days ago, I posted a quote and made a comment about excellence in teaching.  (Why We Have So Few Personal Favorites )  Basically, my proposition was that it is extremely difficult to evaluate the competence and productivity of a teacher because of the number of variables and an inability to control them to a point sufficient to determine what are the tools we could provide the “most effective” teachers to make them better (or any teachers for that matter).
I never gave much thought about teaching until I joined the Army and they insisted I learn, participate in and practice “Performance Oriented Training” (POTs training) when I attended the NCO Academy in Frankfurt, Germany.  Essentially, POTs stipulates that until the student can perform the task, the training has not been effective.  There were three elements:  1)  the instructor demonstrates the task to be performed / explaining the objective of the task, the reason for the task, and each step necessary to complete the task;  2)  the instructor then walks / talks the student through each step as they (the student) follows along with each step;  and, 3)  the instructor asks the student to perform the task independently.  If the student fails in performance (step 3), the instructor must return to element 2.  Re-cycle through elements 2 and 3 until 3 can be accomplished independently.  At that point, the student can perform the task and the training has been effective.  (Of course long term retention of the knowledge / skill is a different matter.)
This training methodology served me very well during my working life / career as I was frequently called upon to instruct on topics in the military, and then as a civilian:  from credit card fraud prevention, to correspondent banking, to numerous Information Technology topics (basic trouble-shooting, using spreadsheets, using word processing applications, server and network administration, setting up databases, conducting data analysis and creating web pages to display the analysis / data).
Rather late in my career, I “discovered” (i.e. read about) Dr Richard P. Feynman (PhD) and his personal learning methodology.  Post-employment (i.e. in retirement), I’ve now watched bits and pieces of Professor Feynman’s lectures (on YouTube) and I believe his methodology is a civilian / academic equivalent of personal POTs training.  That is:  how we should expect to teach ourselves and verify our own knowledge / competency in a subject.  I shudder to think of the number of lectures / classes / training sessions I’ve attended where the instructor either did not have this level of personal expertise or expect the student to demonstrate understanding at the end of the session.  Which, (again) is why we remember our few “great” teachers over our lifetimes.
Disclaimer:  The list of four steps above are available in several books and on the web and the exact wording is neither mine nor exclusive to any specific source so I have not bothered to cite any “original” source.  I apologize in advance if anyone reading this feels I have used their exact language describing Dr. Feynman’s technique.
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Why We Have So Few Personal Favorites

Teaching is the only major occupation of man for which we have not yet developed tools that make an average person capable of competence and performance.  In teaching we rely on the ‘naturals’, the ones who somehow know how to teach.
—     Peter Drucker
[One of the few times I don’t agree with Drucker…   I believe we rely on ‘willing to’ rather than ‘naturals’ to become teachers and then hope most rise to a level of competence and performance.  First, I’m not convinced “average” people are capable of being competent teachers.  I don’t think the ability to teach academic subjects is a skill the average person has.  I do believe that everyone can teach “some” things – just not academic topics, and certainly not at all levels.  Second, I believe “tools” make most people better at “some” things, but do not necessarily make average people competent or able to perform in academic areas.  I’m not convinced tools necessarily make a below-average (whatever that is) person average (whatever that is);  just better than they might have been otherwise.  Third, I’m not convinced we have adequate testing methodologies to rate an academic teacher’s competence and / or performance.  Students are living beings and not subject to controlled experiments as inputs or as outputs.  The “best” we can do is use statistics to estimate student competence / performance under very limited circumstances and, therefore, the results of the comparisons may or may not be widely applicable across wider groups in society.  Even the world’s greatest high school math teacher may not be good (or average) in a grammar school or at a university, let alone at another high school or in other subjects.  Finally, we believe we can use standardized tests to measure the students performance and, therefore, “measure / determine” a teacher’s competence.  This is an assumption which may or may not be valid.  In any case, my understanding is that social / economic banding is the most common important factor for economic progress / success.  This banding has very little to do with an individual teacher’s ability or a student’s performance.  The same teacher can teach multiple siblings at the same school and still end up with a wide variance of sibling performance success.     —    KMAB]
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How Learning Infections Begin

We destroy our children’s songs of existence by giving them inhibitions, teaching them to be cynical, manipulative, and all the rest of it…  You become hardened, but you can find that playfulness again.  We’ve got to find a way to get music and kids together, as well as to teach teachers how to discover their own love of learning.  Then the infectious process begins.
—     Leonard Bernstein
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Horticulture Anyone?

Much education today is monumentally ineffective.  All too often we are giving young people cut flowers when we should be teaching them to grow their own plants.
—    John W. Gardner
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Have Republicans Figured Out Biden Won Yet?

History teaches us that men and nations behave wisely once they have exhausted all other alternatives.
—   Abba Eban
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A Short Count

“Innumeracy: Mathematical Illiteracy And Its Consequences” (1988©)  —  book review
Today’s book review is for:  “Innumeracy: Mathematical Illiteracy And Its Consequences“, written by John Allen Paulos.  The book is an overview of what the author believes are some of the symptoms (and solutions) of “innumeracy” (the math equivalent of illiteracy) in America.  Paulos is a Professor of maths at Temple University (or was at the time of the publication).  He is a bit of a math prodigy (at the very least precocious) and is kind of a cross between Richard Feynman, Malcolm Gladwell and Levitt & Dubner.  Feynman – as a teacher – in converting technical (math) concepts into relatable images, Gladwell in writing for “the general public” consumption, and Levitt & Dubner (of “Freakonomics” fame) in both of the above plus quirky examples to illustrate his point.
This book is a quick (fast read) and short (135 pages) overview of some main concepts in math and how they are poorly taught / translated / communicated to the general public and, hence, the general distaste for maths during school and its avoidance post-formal education whenever possible.
Paulos’ proposition is that because maths are poorly taught, the general public grows up with a fear (and avoidance) of math for the rest of lives.  One of his proposals is to take retired advanced math users (mathematicians, engineers, scientists) and have them teach in schools because the current maths teachers aren’t very good (for a number of reasons) – pun intended.
The author also reviews math concepts: scale (big and little), fractions, ratios, statistics, probabilities and pseudo-sciences.  This overview / review is the strength of the book as it reminded me of many of the areas of math I’ve long since forgotten (for lack of use).
So, is this book any good?  Does it make you feel numerate or innumerate?  Does it help with the issue raised (innumeracy)?  Yes.  Both.  And, no, or at least I don’t think so.  Once I could get past the author’s ego / superiority complex, I actually quite enjoyed the book.  It is a fast read and he does use his examples in a clear and sometimes humorous fashion.  The text made me feel numerate.  The work through examples innumerate.  A few of the paragraphs had to be re-read to make sure I followed the explanations for why he was doing a particular calculation.  For example, how many days is a million seconds?  The author says eleven-ish.  So, then how long is a billion seconds?  Again, thirty something years.  Now, the author actually worked out the numbers and provided the answers.  The problem?  Well, for me, the answer is 11(-ish) thousand days.  I would never arbitrarily convert days to years.  Not that I couldn’t;  just that I wouldn’t.  Why would I, unless specifically asked?  And, for most purposes, I would have ball-parked it (1,000 days is almost 3 years, times 11 is “about” 33 years).  It would not be entirely accurate, but even then, the author didn’t state he was accounting for leap years in his own calculations.  His point was we “all” know how much a second is.  What we don’t know (have a feeling for) is how big a number is a billion (or a million).  My point is I’m not sure if my reaction means I’m personally numerate or innumerate.  And, finally, simply pointing out a problem isn’t the same as offering a viable solution.  I don’t think placing retired math users in schools is a workable solution.  Teaching (across all of the non-adult years) is an art as much as it is a skill.  Yes, you must be grounded in the material, but you must also be enthusiastic (about the subject and teaching) and relatable.  I’m not convinced there is a vast pool of retired engineers and scientists just dying to teach grammar, middle and high school students (and each group has different requirements).
Final recommendation:  Strong to highly recommended.  As an overview of maths topics for the general public, I think this is a very valuable book.  It is brief and has interesting examples.  It is probably too simple for folks with college level math skills.  It is probably too difficult for the truly innumerate.  But, I think there is a wide, flat(ish) bell shaped curve of folks out there (probably 2 standard deviations on either side of the mean) who would gain from reading this book.  Those below the mean because the writing and examples are clear and can be followed along with.  Those above the curve, because the book will remind you how much you’ve forgotten since leaving school.  I just wish the author had been a bit less patronizing of us non-math prodigies.
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Accustomed To It

“I wish to become a teacher of the Truth.”
“Are you prepared to be ridiculed, ignored and starving till you are forty-five?”
“I am.  But tell me:  What will happen after I am forty-five?”
“You will have grown accustomed to it.”
—    Anthony De Mello
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Gratitude And Warmth

One looks back with appreciation to the brilliant teachers, but with gratitude to those who touched our human feelings.  The curriculum is so much necessary raw material, but warmth is the vital element for the growing plant and for the soul of the child.
—    Carl Gustav Jung
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Shedding Light

If a man is to shed the light of the sun upon other men, he must first of all have it within himself.
—    Romain Rolland
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Reinforced Learning

To teach is to learn twice.
—    Joseph Joubert
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Nothing Is Known Absolutely

Science is a way to teach how something gets to be known, what is not known, to what extent things are known (for nothing is known absolutely), how to handle doubt and uncertainty, what the rules of evidence are, how to think about things so that judgments can be made, how to distinguish truth from fraud, and from show.
—    Richard P. Feynman
Quoted by James Gleick, in his book:  “Genius“
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Nurture Tolerance

…What drove me to teach were two sparks.  The spark in a student’s eye when they grasped their way with confidence; and the spark in my eye when a student revealed a different perspective to mine.  That’s why I loved being an English teacher.  It was all about sharing different interpretations, perspectives and nuances that lay within a landscape of words speaking truths only made real in someone else’s mind.  My role was to enable that thought freedom and to nurture tolerance.  My job was to allow people unique views in on the worlds we studied each day and for my eyes to be widened by their perspective.  Learning happened all round and, if I ever did my job right, on all levels too.
—    From a blog I follow:  “The Bamboo Principle“, located at: http://thebambooprinciple.wordpress.com/
The specific post was: http://thebambooprinciple.wordpress.com/2013/10/08/a-job-of-it/
[Another great blog to check out if you haven’t already…  And, yes, back in 2010, I still didn’t know about scheduling posts.  In a way, it’s nice to be reminded we’re all beginners at some point.   —    KMAB]
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What Is Your Canvas?

Looking back, perhaps the lesson I would draw is this:  If you don’t love it, don’t do it.  I loved it — teaching people how to reach in deep to fulfill their potential, how to become great.  And when you do that with a group, you, as the leader, enjoy the thrill of creating a great team.  For me it was like creating a work of art.  Only instead of painting on a canvas, I had the great joy of creating in collaboration with others.
—    Bill Walsh
From his book:  “The Score Takes Care Of Itself“
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